An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh
The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteri...
Uloženo v:
| Vydáno v: | Numerical algorithms Ročník 81; číslo 2; s. 465 - 487 |
|---|---|
| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer US
01.06.2019
Springer Nature B.V |
| Témata: | |
| ISSN: | 1017-1398, 1572-9265 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteriori error estimate which will lead to a layer adaptive mesh by moving a fixed number of mesh points. It is theoretically shown that the layer adaptive solution on the a posteriori generated mesh will uniformly converge to the exact solution with optimal order accuracy where the optimality is measured with respect to the continuous problem discretization. The comparison results with the existing methods based on a priori meshes show that the proposed method on the a posteriori mesh is highly effective. |
|---|---|
| AbstractList | The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers. Here, we provide an a posteriori based convergence analysis for the adaptation of these layer phenomena. We derive a parameter uniform a posteriori error estimate which will lead to a layer adaptive mesh by moving a fixed number of mesh points. It is theoretically shown that the layer adaptive solution on the a posteriori generated mesh will uniformly converge to the exact solution with optimal order accuracy where the optimality is measured with respect to the continuous problem discretization. The comparison results with the existing methods based on a priori meshes show that the proposed method on the a posteriori mesh is highly effective. |
| Author | Das, Pratibhamoy |
| Author_xml | – sequence: 1 givenname: Pratibhamoy surname: Das fullname: Das, Pratibhamoy email: pratibhamoy@gmail.com, pratibhamoy@iitp.ac.in organization: Department of Mathematics, Indian Institute of Technology |
| BookMark | eNp9kM1q3TAQhUVIIT_tA3Qn6NqN5D9ZyxCSJhDoJnsxlke3Cr6SM5IDfoU8dZTeQiCQgkBncb45M-eMHYcYkLHvUvyUQqiLJKVQXSXkUImuU1V7xE5lp-pK1313XLSQqpKNHk7YWUqPQhSqVqfs5TJw4EtMGclH8nyEhBO3MTwj7TBY5BBg3pJP3EUq3hI8-4BAPPmwW2egeeMLUl5pLGTayqg9j45POMPGJ-8cEobsYeb4tEL2MSQeS2x5EyzZPyPfY_rzlX1xMCf89u8_Zw831w9Xt9X97193V5f3lW1kn6u2G1QR1ko9tbYH6EfhdKtbN41WWatLnlYAWITWnZjG1iqntBu0lV3dnLMfh7ELxacVUzaPcaVyYzK1lkPfN7puikseXJZiSoTOLOT3QJuRwrw1bg6Nm9K4eWvctIVRHxjr8997M4Gf_0vWBzKVlLBDet_pc-gVVhaa9A |
| CitedBy_id | crossref_primary_10_1007_s10910_020_01190_7 crossref_primary_10_1007_s12190_021_01613_x crossref_primary_10_1002_mma_10070 crossref_primary_10_1016_j_cam_2020_113116 crossref_primary_10_1016_j_apnum_2024_09_020 crossref_primary_10_1016_j_cam_2020_113115 crossref_primary_10_1002_mma_10393 crossref_primary_10_1111_sapm_12763 crossref_primary_10_1007_s12190_024_02226_w crossref_primary_10_1007_s10910_024_01634_4 crossref_primary_10_1007_s10910_024_01638_0 crossref_primary_10_3390_sym12010136 crossref_primary_10_1002_mma_10358 crossref_primary_10_1002_mma_7369 crossref_primary_10_1016_j_apnum_2022_11_003 crossref_primary_10_1155_2020_8829092 crossref_primary_10_1007_s13137_019_0129_3 crossref_primary_10_1007_s40010_020_00723_8 crossref_primary_10_1007_s12190_024_02312_z crossref_primary_10_1080_15502287_2021_1948148 crossref_primary_10_3934_nhm_2025024 crossref_primary_10_1007_s40819_023_01543_1 crossref_primary_10_1007_s11075_018_00652_z crossref_primary_10_1007_s11766_024_4148_y crossref_primary_10_1007_s13137_023_00222_z crossref_primary_10_1140_epjs_s11734_024_01267_3 crossref_primary_10_1016_j_bulsci_2025_103637 crossref_primary_10_1002_fld_5201 crossref_primary_10_1016_j_apnum_2023_10_003 crossref_primary_10_1002_mma_10461 crossref_primary_10_1002_mma_9460 crossref_primary_10_1016_j_cam_2025_116797 crossref_primary_10_1016_j_cam_2025_116754 crossref_primary_10_1002_mma_9381 crossref_primary_10_1016_j_compbiomed_2024_108756 crossref_primary_10_1002_mma_10464 crossref_primary_10_1007_s10910_022_01393_0 crossref_primary_10_1007_s13398_023_01397_8 crossref_primary_10_1007_s12190_024_02252_8 crossref_primary_10_1002_mma_10986 crossref_primary_10_1016_j_amc_2020_125677 crossref_primary_10_1016_j_camwa_2025_05_019 crossref_primary_10_1002_mma_10984 crossref_primary_10_1007_s11075_019_00795_7 crossref_primary_10_1002_mma_7358 crossref_primary_10_1002_mma_9778 crossref_primary_10_1016_j_chaos_2025_116456 crossref_primary_10_1080_00207160_2019_1673892 crossref_primary_10_1007_s40314_021_01733_x crossref_primary_10_1007_s12190_024_02173_6 crossref_primary_10_1140_epjs_s11734_024_01254_8 crossref_primary_10_1007_s12190_023_01900_9 crossref_primary_10_1016_j_matcom_2021_05_005 crossref_primary_10_1007_s12591_022_00593_z crossref_primary_10_1002_cmm4_1047 crossref_primary_10_1002_cmm4_1201 crossref_primary_10_1002_fld_5294 crossref_primary_10_1016_j_apnum_2019_08_028 crossref_primary_10_1108_EC_08_2018_0337 crossref_primary_10_1016_j_apnum_2024_09_001 crossref_primary_10_1080_02331934_2025_2534119 crossref_primary_10_1155_2020_4879723 crossref_primary_10_1016_j_amc_2021_126385 crossref_primary_10_1016_j_matcom_2022_02_018 crossref_primary_10_1007_s12190_025_02601_1 crossref_primary_10_1007_s40010_020_00687_9 crossref_primary_10_1016_j_matcom_2025_02_023 crossref_primary_10_1080_27684830_2023_2286670 crossref_primary_10_1155_2022_9291834 crossref_primary_10_1002_mma_10018 crossref_primary_10_1007_s11144_024_02570_9 crossref_primary_10_1007_s40863_024_00424_9 crossref_primary_10_1007_s40010_023_00852_w crossref_primary_10_1007_s00500_023_08057_4 crossref_primary_10_1002_mma_7904 crossref_primary_10_1007_s11075_021_01205_7 crossref_primary_10_1007_s12190_023_01977_2 crossref_primary_10_1186_s13660_024_03235_w crossref_primary_10_1016_j_matcom_2021_10_029 crossref_primary_10_1515_nleng_2024_0074 crossref_primary_10_1007_s40314_022_01928_w crossref_primary_10_1016_j_camwa_2023_04_004 crossref_primary_10_1016_j_camwa_2023_09_008 crossref_primary_10_1007_s12591_024_00699_6 crossref_primary_10_1080_10236198_2022_2062235 crossref_primary_10_1515_nleng_2024_0070 crossref_primary_10_1007_s12190_020_01396_7 crossref_primary_10_1007_s11075_021_01147_0 crossref_primary_10_1016_j_cam_2023_115441 crossref_primary_10_1016_j_cam_2020_113167 crossref_primary_10_3390_app10145019 crossref_primary_10_1007_s11144_023_02546_1 crossref_primary_10_1007_s12591_021_00577_5 crossref_primary_10_1007_s11075_024_01918_5 crossref_primary_10_1007_s11075_024_01804_0 crossref_primary_10_1016_j_camwa_2023_09_013 |
| Cites_doi | 10.1090/S0025-5718-08-02125-X 10.1137/S0036139992228119 10.1016/S0022-247X(03)00193-8 10.1007/978-1-4419-7916-2 10.1137/S003614290138471X 10.1080/10236190903305450 10.1016/j.cam.2010.05.006 10.1007/s10543-015-0577-6 10.1093/imanum/21.1.349 10.1007/s11075-009-9306-z 10.1093/imanum/drp052 10.1016/S0168-9274(99)00065-3 10.1007/s10543-015-0559-8 10.1137/S0036142900368642 10.1007/s11075-005-7079-6 10.1016/j.camwa.2006.07.009 10.1137/S0036139992228120 10.1016/j.cam.2017.11.026 10.1080/00207160.2016.1184263 |
| ContentType | Journal Article |
| Copyright | Springer Science+Business Media, LLC, part of Springer Nature 2018 Springer Science+Business Media, LLC, part of Springer Nature 2018. |
| Copyright_xml | – notice: Springer Science+Business Media, LLC, part of Springer Nature 2018 – notice: Springer Science+Business Media, LLC, part of Springer Nature 2018. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1007/s11075-018-0557-4 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering Collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics Computer Science |
| EISSN | 1572-9265 |
| EndPage | 487 |
| ExternalDocumentID | 10_1007_s11075_018_0557_4 |
| GroupedDBID | -4Z -59 -5G -BR -EM -~C .86 .DC .VR 06D 0R~ 0VY 123 1N0 203 29N 2J2 2JN 2JY 2KG 2KM 2LR 2~H 30V 4.4 406 408 409 40D 40E 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYZH ABAKF ABBBX ABBXA ABDZT ABECU ABFTD ABFTV ABHLI ABHQN ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABSXP ABTEG ABTHY ABTKH ABTMW ABWNU ABXPI ACAOD ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACZOJ ADHHG ADHIR ADIMF ADINQ ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEFQL AEGAL AEGNC AEJHL AEJRE AEMSY AENEX AEOHA AEPYU AESKC AETLH AEVLU AEXYK AFBBN AFLOW AFQWF AFWTZ AFZKB AGAYW AGDGC AGJBK AGMZJ AGQEE AGQMX AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHSBF AHYZX AIAKS AIGIU AIIXL AILAN AITGF AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARMRJ ASPBG AVWKF AXYYD AYJHY AZFZN B-. BA0 BDATZ BGNMA BSONS CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ6 GQ7 GQ8 GXS HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ KDC KOV LAK LLZTM M4Y M7S MA- N9A NB0 NPVJJ NQJWS NU0 O93 O9G O9I O9J OAM P19 P2P P9O PF0 PT4 PT5 QOK QOS R89 R9I RHV RNS ROL RPX RSV S16 S27 S3B SAP SCJ SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 TSG TSK TSV TUC U2A UG4 UOJIU UTJUX VC2 W23 W48 WK8 YLTOR Z45 Z7R Z7X Z7Z Z81 Z83 Z88 Z8M Z8R Z8T Z8W Z92 ZMTXR ~EX -Y2 1SB 2.D 2P1 2VQ 5QI AAOBN AAPKM AARHV AAYTO AAYXX ABBRH ABDBE ABFSG ABJCF ABQSL ABRTQ ABULA ACBXY ACSTC ADHKG AEBTG AEFIE AEKMD AEZWR AFDZB AFEXP AFFHD AFGCZ AFHIU AFKRA AFOHR AGGDS AGQPQ AHPBZ AHWEU AIXLP AJBLW ARAPS ATHPR AYFIA BBWZM BENPR BGLVJ CAG CCPQU CITATION COF H13 HCIFZ K7- KOW N2Q NDZJH O9- OVD PHGZM PHGZT PQGLB PTHSS R4E RNI RZC RZE RZK S1Z S26 S28 SCLPG T16 TEORI UZXMN VFIZW VOH ZY4 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c316t-4587316cc19d4c6aa6b0f9494fdbc7cc9ffe97aae9ff9950db4c7f79f89c1523 |
| IEDL.DBID | K7- |
| ISICitedReferencesCount | 127 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000468607000004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1017-1398 |
| IngestDate | Wed Nov 05 03:34:05 EST 2025 Sat Nov 29 01:34:45 EST 2025 Tue Nov 18 21:29:40 EST 2025 Fri Feb 21 02:32:27 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 2 |
| Keywords | 35F25 65L05 A posteriori based convergence analysis Nonlinear equations Optimal convergent solution 35F20 Singular perturbation 34A34 Multiple layer phenomena 65Y20 Interior layer 34L30 Multi-scale phenomena Moving mesh algorithm A priori and a posteriori meshes 65L50 Delay problem System of differential equations 65J15 65L10 |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c316t-4587316cc19d4c6aa6b0f9494fdbc7cc9ffe97aae9ff9950db4c7f79f89c1523 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2918663923 |
| PQPubID | 2043837 |
| PageCount | 23 |
| ParticipantIDs | proquest_journals_2918663923 crossref_primary_10_1007_s11075_018_0557_4 crossref_citationtrail_10_1007_s11075_018_0557_4 springer_journals_10_1007_s11075_018_0557_4 |
| PublicationCentury | 2000 |
| PublicationDate | 20190601 2019-6-00 |
| PublicationDateYYYYMMDD | 2019-06-01 |
| PublicationDate_xml | – month: 6 year: 2019 text: 20190601 day: 1 |
| PublicationDecade | 2010 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Numerical algorithms |
| PublicationTitleAbbrev | Numer Algor |
| PublicationYear | 2019 |
| Publisher | Springer US Springer Nature B.V |
| Publisher_xml | – name: Springer US – name: Springer Nature B.V |
| References | Vulanovic (CR21) 2001; 21 Amiraliyev, Erdogan (CR3) 2009; 52 Kopteva (CR15) 2001; 39 Kellogg, Linss, Stynes (CR14) 2008; 77 Kopteva, Stynes (CR16) 2001; 39 Amiraliyev, Erdogan (CR2) 2007; 53 Zhang, Naidu, Zou (CR23) 2014; 9 Ha, Mehrman (CR10) 2016; 56 CR7 Kopteva, Madden, Stynes (CR17) 2005; 3 Cen, Le, Xu (CR6) 2010; 234 CR9 Huang, Russell (CR12) 2011 Das, Mehrmann (CR8) 2016; 56 Xu, Huang, Russell, Williams (CR22) 2011; 31 Abbas (CR1) 2011; 2011 Hemavathi, Bhuvaneswari, Valamarthi, Miller (CR11) 2007; 191 Kadalbajoo, Patidar, Sharma (CR13) 2006; 182 Lange, Miura (CR18) 1994; 54 Bashier, Patidar (CR4) 2011; 17 Beckett, Mackenzie (CR5) 2000; 35 Tian, Kuang (CR20) 2003; 281 Lange, Miura (CR19) 1994; 54 N Kopteva (557_CR15) 2001; 39 Z Cen (557_CR6) 2010; 234 N Kopteva (557_CR16) 2001; 39 R Vulanovic (557_CR21) 2001; 21 S Abbas (557_CR1) 2011; 2011 EBM Bashier (557_CR4) 2011; 17 RB Kellogg (557_CR14) 2008; 77 X Xu (557_CR22) 2011; 31 MK Kadalbajoo (557_CR13) 2006; 182 557_CR9 P Ha (557_CR10) 2016; 56 H Tian (557_CR20) 2003; 281 557_CR7 CG Lange (557_CR18) 1994; 54 Y Zhang (557_CR23) 2014; 9 GM Amiraliyev (557_CR2) 2007; 53 P Das (557_CR8) 2016; 56 N Kopteva (557_CR17) 2005; 3 CG Lange (557_CR19) 1994; 54 W Huang (557_CR12) 2011 MG Beckett (557_CR5) 2000; 35 S Hemavathi (557_CR11) 2007; 191 GM Amiraliyev (557_CR3) 2009; 52 |
| References_xml | – volume: 77 start-page: 2085 year: 2008 end-page: 2096 ident: CR14 article-title: A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions publication-title: Math. Comput. doi: 10.1090/S0025-5718-08-02125-X – volume: 54 start-page: 273 year: 1994 end-page: 283 ident: CR19 article-title: Singular perturbation analysis of boundary value problems for differential difference equations. vi. small shifts with rapid oscillations publication-title: SIAM. J. Appl. Math. doi: 10.1137/S0036139992228119 – volume: 281 start-page: 678 year: 2003 end-page: 696 ident: CR20 article-title: Asymptotic expansions for the solution of singularly perturbed delay differential equations publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(03)00193-8 – year: 2011 ident: CR12 publication-title: Adaptive Moving Mesh Methods doi: 10.1007/978-1-4419-7916-2 – volume: 191 start-page: 1 year: 2007 end-page: 11 ident: CR11 article-title: A parameter uniform numerical method for a system of singularly perturbed ordinary differential equations publication-title: Appl. Math. Comput. – volume: 39 start-page: 1446 year: 2001 end-page: 1467 ident: CR16 article-title: A robust adapive method for a quasilinear one-dimensional convection diffusion problem publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614290138471X – volume: 17 start-page: 779 year: 2011 end-page: 794 ident: CR4 article-title: A second-order fitted operator finite difference method for a singularly perturbed delay parabolic partial differential equation publication-title: J. Difference Equ. Appl. doi: 10.1080/10236190903305450 – volume: 234 start-page: 3445 year: 2010 end-page: 3457 ident: CR6 article-title: A second-order hybrid difference scheme for a system of singularly perturbed initial value problems publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2010.05.006 – volume: 56 start-page: 633 year: 2016 end-page: 657 ident: CR10 article-title: Analysis and numerical solution of linear delay differential-algebraic equations publication-title: BIT Numer. Math. doi: 10.1007/s10543-015-0577-6 – volume: 182 start-page: 119 year: 2006 end-page: 139 ident: CR13 article-title: ε-uniformly convergent fitted methods for the numerical solution of the problems arising from singularly perturbed general ddes publication-title: Appl. Math. Comput. – volume: 21 start-page: 349 year: 2001 end-page: 366 ident: CR21 article-title: A priori meshes for singularly perturbed quasilinear two point boundary value problems publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/21.1.349 – volume: 2011 start-page: 1 year: 2011 end-page: 11 ident: CR1 article-title: Existence of solutions to fractional order ordinary and delay differential equations and applications publication-title: Electron. J. Differ. Equ. – ident: CR9 – volume: 52 start-page: 663 year: 2009 end-page: 675 ident: CR3 article-title: A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations publication-title: Numer. Algorithms doi: 10.1007/s11075-009-9306-z – volume: 31 start-page: 580 year: 2011 end-page: 596 ident: CR22 article-title: Convergence of de Boor’s algorithm for the generation of equidistributing meshes publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drp052 – volume: 35 start-page: 87 year: 2000 end-page: 109 ident: CR5 article-title: Convergence analysis of finite difference approximations on equidistribted grids to a singularly perturbed boundary value problem publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(99)00065-3 – ident: CR7 – volume: 56 start-page: 51 year: 2016 end-page: 76 ident: CR8 article-title: Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters publication-title: BIT Numer. Math. doi: 10.1007/s10543-015-0559-8 – volume: 39 start-page: 423 year: 2001 end-page: 441 ident: CR15 article-title: Maximum norm a posteriori error estimates for a one-dimensional convection diffusion problem publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142900368642 – volume: 3 start-page: 305 year: 2005 end-page: 322 ident: CR17 article-title: Grid equidistribution for reaction- diffusion problems in one dimension publication-title: Numer. Algorithms doi: 10.1007/s11075-005-7079-6 – volume: 53 start-page: 1251 year: 2007 end-page: 1259 ident: CR2 article-title: Uniform numerical method for singularly perturbed delay differential equations publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.07.009 – volume: 54 start-page: 249 year: 1994 end-page: 272 ident: CR18 article-title: Singular perturbation analysis of boundary value problems for differential difference equations. v. small shifts with layer behavior publication-title: SIAM. J. Appl. Math. doi: 10.1137/S0036139992228120 – volume: 9 start-page: 1 issue: 1 year: 2014 end-page: 36 ident: CR23 article-title: Singular perturbations and time scales in control theory and applications: an overview 2002-2012 publication-title: Int. J. Inf. Syst. Sci. – volume: 17 start-page: 779 year: 2011 ident: 557_CR4 publication-title: J. Difference Equ. Appl. doi: 10.1080/10236190903305450 – volume: 54 start-page: 273 year: 1994 ident: 557_CR19 publication-title: SIAM. J. Appl. Math. doi: 10.1137/S0036139992228119 – volume: 3 start-page: 305 year: 2005 ident: 557_CR17 publication-title: Numer. Algorithms doi: 10.1007/s11075-005-7079-6 – volume: 54 start-page: 249 year: 1994 ident: 557_CR18 publication-title: SIAM. J. Appl. Math. doi: 10.1137/S0036139992228120 – volume: 31 start-page: 580 year: 2011 ident: 557_CR22 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/drp052 – volume: 182 start-page: 119 year: 2006 ident: 557_CR13 publication-title: Appl. Math. Comput. – volume: 39 start-page: 1446 year: 2001 ident: 557_CR16 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S003614290138471X – volume: 21 start-page: 349 year: 2001 ident: 557_CR21 publication-title: IMA J. Numer. Anal. doi: 10.1093/imanum/21.1.349 – volume: 2011 start-page: 1 year: 2011 ident: 557_CR1 publication-title: Electron. J. Differ. Equ. – volume: 35 start-page: 87 year: 2000 ident: 557_CR5 publication-title: Appl. Numer. Math. doi: 10.1016/S0168-9274(99)00065-3 – ident: 557_CR9 doi: 10.1016/j.cam.2017.11.026 – volume: 77 start-page: 2085 year: 2008 ident: 557_CR14 publication-title: Math. Comput. doi: 10.1090/S0025-5718-08-02125-X – volume: 281 start-page: 678 year: 2003 ident: 557_CR20 publication-title: J. Math. Anal. Appl. doi: 10.1016/S0022-247X(03)00193-8 – volume: 9 start-page: 1 issue: 1 year: 2014 ident: 557_CR23 publication-title: Int. J. Inf. Syst. Sci. – volume: 53 start-page: 1251 year: 2007 ident: 557_CR2 publication-title: Comput. Math. Appl. doi: 10.1016/j.camwa.2006.07.009 – volume: 56 start-page: 633 year: 2016 ident: 557_CR10 publication-title: BIT Numer. Math. doi: 10.1007/s10543-015-0577-6 – volume: 234 start-page: 3445 year: 2010 ident: 557_CR6 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2010.05.006 – ident: 557_CR7 doi: 10.1080/00207160.2016.1184263 – volume-title: Adaptive Moving Mesh Methods year: 2011 ident: 557_CR12 doi: 10.1007/978-1-4419-7916-2 – volume: 56 start-page: 51 year: 2016 ident: 557_CR8 publication-title: BIT Numer. Math. doi: 10.1007/s10543-015-0559-8 – volume: 191 start-page: 1 year: 2007 ident: 557_CR11 publication-title: Appl. Math. Comput. – volume: 39 start-page: 423 year: 2001 ident: 557_CR15 publication-title: SIAM J. Numer. Anal. doi: 10.1137/S0036142900368642 – volume: 52 start-page: 663 year: 2009 ident: 557_CR3 publication-title: Numer. Algorithms doi: 10.1007/s11075-009-9306-z |
| SSID | ssj0010027 |
| Score | 2.5332623 |
| Snippet | The present work considers a nonlinear system of singularly perturbed delay differential equation whose each component of the solution has multiple layers.... |
| SourceID | proquest crossref springer |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 465 |
| SubjectTerms | Algebra Algorithms Computer Science Convergence Differential equations Error analysis Exact solutions Mesh generation Nonlinear systems Numeric Computing Numerical Analysis Optimization Original Paper Partial differential equations Theory of Computation |
| SummonAdditionalLinks | – databaseName: SpringerLINK Contemporary 1997-Present dbid: RSV link: http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1La9wwEB6aNIf00LR50G3TMoecWgR-aG3NMZSGHtpQmhByM7IeZGGzu7G3hf0L_dUd2dYuLW0gAR-MLcmCkWY-eWa-ATghT3VG3giVyULI0qZCFaURNk9cmSQ2V11-xdWX8vxcXV_TtyGPu43R7tEl2WnqTbIbn1RCoJkSgTdKyC14ytZOhd34_eJq7ToIB63Oxcnql-GNiq7Mfw3xpzHaIMy_nKKdrTnbe9QsX8DzAVriab8WXsITN9uHvQFm4rCJW34UKznEZ_vw7OuavbU9gF-nM9S4COkfzWTeTDCYOotdgHqXq-lQD1wmyJiX2856wg3dYPj1ECJbpytcuIbtWc09e7ponHsMnJQrjFVZWLtM0d31bOMtzvmzfFm9CDoYb117cwiXZ58uP34WQ80GYfK0WAo5VqEWljEpWWkKrYs68SRJelub0hji8anU2vEN0TixtTSlL8krMgwl8iPY5im7V4ApudynhS285f6sWC05a7OxCyc4nY1HkETZVWbgMw9lNabVhok5yKJiWVRBFpUcwft1l0VP5nFf4-O4IKphX7dVRoEgkDFlPoIPcQFsXv93sNcPav0GdhmXUR-Rdgzby-aHews75udy0jbvuuX-G5OP--A priority: 102 providerName: Springer Nature |
| Title | An a posteriori based convergence analysis for a nonlinear singularly perturbed system of delay differential equations on an adaptive mesh |
| URI | https://link.springer.com/article/10.1007/s11075-018-0557-4 https://www.proquest.com/docview/2918663923 |
| Volume | 81 |
| WOSCitedRecordID | wos000468607000004&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAVX databaseName: SpringerLINK Contemporary 1997-Present customDbUrl: eissn: 1572-9265 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0010027 issn: 1017-1398 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9RAEB-09UEfrFbF03rsg0_KYj72spknqdIiqEdpS-lb2OwHFs67NDmF_gv-1c4kmzsU7IsQQiC7k4WZzMzuzPwG4DUGrDMMVpaZKqTSLpVloa10eeJ1kri87OsrLr7o-by8vMSTeODWxbTKUSf2itqtLJ-Rv8uQodnImufvm2vJXaM4uhpbaNyF3TTLUpbzz1puogi85-qjnaSJydMpx6hmXzpH-x5OWyslo1BJ9add2jqbf8VHe7NzvPe_C34ED6PDKQ4HCXkMd_xyH_ai8ynir93tw4OvGwDX7gn8OlwKIxquAGmviKpga-dEn6Pel2t6YSKciSC3l8YuB8wN0wo-feDk1sWNaHxLJq2mmQNitFgFwbCUN2JszEIKZiH89QA43okVfZYuZxpWw-K77749hfPjo_OPn2Rs2yBtnhZrqWYlt8OyNkWnbGFMUScBFargaqutRaKP2hhPD4izxNXK6qAxlGjJm8ifwQ4t2T8HkaLPQ1q4IjiaT7rVoXcum3nexJlsNoFk5FllI6Q5d9ZYVFswZmZzRWyumM2VmsCbzZRmwPO4bfDByNoq_tpdteXrBN6OwrF9_U9iL24n9hLuky-GQxbaAeys2x_-FdyzP9dXXTuF3Q9H85PTaS_fU05QPaP76dnFbyNaA7E |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V3NbtQwEB6VggQcKBQQSwv4ABeQ1fx4k_hQoQqoWnW7QmKFerMc_4hKy26aLKB9Bd6l79gZJ9kVSPTWA1IOkWI7ifNlZuyZ-QbgtfSyTKQ3vEhExkVuY15kueE2jVweRTYtQn7F11E-HhdnZ_LzBlz2uTAUVtnLxCCo7dzQHvleIomaDbV5-r664FQ1iryrfQmNFhYnbvkLl2zN_vFH_L5vkuTw0-TDEe-qCnCTxtmCi2FB1ZqMiaUVJtM6KyMvhRTeliY3RnrvZK61wxMph5Ethcl9Ln0hDSq7FIe9BbcFCf8QKfhl5bSgJV5wrqLgR8Oq6J2oIVMPl1kUJVdwIr3i4k81uLZt_3LHBi13uPWfzc9DeNCZ0-ygxf8j2HCzbdjqTGvWCa5mG-6fruhpm8fw-2DGNKsov6U-x5dgpMstCxH4IRnVMd2RtTA06rHtrGUU0TWjvRUK3Z0uWeVqVNgl9mz5sNncMyLdXLK-7AyKzylzFy2desPmeFs8rK5IybDvrvn2BCY3MT1PYRMf2T0DFkuX-jizmbfYHzWHlc7aZOhoiaqT4QCiHiLKdITtVDdkqtZU04QqhahShColBvB21aVq2Uqua7zbI0l1gqtRaxgN4F2PxfXlfw72_PrBXsHdo8npSI2Oxyc7cA-tTtnG2-3C5qL-4V7AHfNzcd7UL8MvxUDdMESvALeIXx0 |
| linkToPdf | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3da9RAEB9qFdEHq1XxtOo--KQszcdeknkstkeL9ShYSt_CZj_w4LyLySn0X_CvdibJ3qHUghTyEJLdzcLszv4mM_MbgHfosUrQG1kkKpMqt7EsstxIm0YujyKbFl1-xcVpPp0Wl5d4NtQ5bUO0e3BJ9jkNzNK0WO3X1u9vEt_IauGgs0Iyh5RUd-Cu4ppBbK5_uVi7Edjo6tydpIoJ6hTBrXndEH8eTBu0-ZeDtDt3Jju3nvFjeDRATnHQr5EnsOUWu7AzwE8xbO6WHoUKD-HZLjz8vGZ1bZ_Cr4OF0KLmtJBmtmxmgo9AK7rA9S6H0wk9cJwIwsLUdtETcehG8C8JjnidX4naNXTOVdSzp5EWSy-Yq_JKhGotpHXmwn3vWchbsaTP0mV1zbpZfHPt12dwPjk6_3gsh1oO0qRxtpJqXHCNLGNitMpkWmdV5FGh8rYyuTFI42OutaMbxHFkK2Vyn6Mv0BDESJ_DNk3ZvQARo0t9nNnMW-pPCteiszYZO7bsdDIeQRTkWJqB55zLbczLDUMzy6IkWZQsi1KN4P26S92TfNzUeC8sjnLY722ZIBMHEtZMR_AhLIbN638O9vK_Wr-F-2eHk_L0ZPrpFTwg6IZ90NoebK-aH-413DM_V7O2edPtgt-sFQe3 |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=An+a+posteriori+based+convergence+analysis+for+a+nonlinear+singularly+perturbed+system+of+delay+differential+equations+on+an+adaptive+mesh&rft.jtitle=Numerical+algorithms&rft.au=Das%2C+Pratibhamoy&rft.date=2019-06-01&rft.issn=1017-1398&rft.eissn=1572-9265&rft.volume=81&rft.issue=2&rft.spage=465&rft.epage=487&rft_id=info:doi/10.1007%2Fs11075-018-0557-4&rft.externalDBID=n%2Fa&rft.externalDocID=10_1007_s11075_018_0557_4 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1017-1398&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1017-1398&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1017-1398&client=summon |